pareto1(VGAM)
pareto1()所属R语言包：VGAM
Pareto and Truncated Pareto Distribution Family Functions
帕累托和截断Pareto分布家庭功能
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Estimates one of the parameters of the Pareto(I) distribution by maximum likelihood estimation. Also includes the upper truncated Pareto(I) distribution.
估计帕累托（I）分布的最大似然估计的参数之一。此外，还包括上截断帕雷托分布（I）。
用法----------Usage----------
pareto1(lshape = "loge", earg = list(), location = NULL)
tpareto1(lower, upper, lshape = "loge", earg = list(), ishape = NULL,
imethod = 1)
参数----------Arguments----------
参数：lshape
Parameter link function applied to the parameter k. See Links for more choices. A log link is the default because k is positive.
参数链接功能的参数k。见Links更多的选择。的log链接是默认的，因为“k是积极的。
参数：earg
List. Extra argument for the link. See earg in Links for general information.
列表。额外的参数的链接。见earg中Links的一般信息。
参数：lower, upper
Numeric. Lower and upper limits for the truncated Pareto distribution. Each must be positive and of length 1. They are called alpha and U below.
数字。截断Pareto分布的上限和下限。每个人都必须是积极的，长度为1。他们被称为alpha和U下面。
参数：ishape
Numeric. Optional initial value for the shape parameter. A NULL means a value is obtained internally. If failure to converge occurs try specifying a value, e.g., 1 or 2.
数字。可选的形状参数的初始值。 ANULL是指内部得到的值。如果出现收敛失败尝试指定一个值，例如1或2。
参数：location
Numeric. The parameter alpha below. If the user inputs a number then it is assumed known with this value. The default means it is estimated by maximum likelihood estimation, which means min(y) where y is the response vector.
数字。参数alpha下面。如果用户输入一个号码，那么它被假定与此值已知。默认意味着它是估计的最大似然估计，这意味着min(y)y是响应向量。
参数：imethod
An integer with value 1 or 2 which specifies the initialization method. If failure to converge occurs try the other value, or else specify a value for ishape.
一个整数，值1或2指定的初始化方法。如果收敛失败发生的其他值，否则指定的值ishape。
Details
详细信息----------Details----------
A random variable Y has a Pareto distribution if
随机变量Y如果有一个帕累托分布
for some positive k and C. This model is important in many applications due to the power law probability tail, especially for large values of y.
一些积极的k和C。这种模式是很重要的，在许多应用中，由于功法概率尾巴，特别是对于大值y。
The Pareto distribution, which is used a lot in economics, has a probability density function that can be written
帕累托分布，这是用了很多在经济学中，有一个概率密度函数可以写
for 0< alpha < y and k>0. The alpha is known as the location parameter, and k is known as the shape parameter. The mean of Y is alpha*k/(k-1) provided k > 1. Its variance is alpha^2 k /((k-1)^2 (k-2)) provided k > 2.
0< alpha < y和k>0。被称为alpha的位置参数，和k被称为形状参数。 Y的平均alpha*k/(k-1)提供k > 1。方差为alpha^2 k /((k-1)^2 (k-2))提供k > 2。
The upper truncated Pareto distribution has a probability density function that can be written
上部截断Pareto分布的概率密度函数，可以写入
for 0< alpha < y < U < Inf and k>0. Possibly, better names for k are the index and tail parameters. Here, alpha and U are known. The mean of Y is k * lower^k * (U^(1-k)-alpha^(1-k)) / ((1-k) * (1-(alpha/U)^k)).
0< alpha < y < U < Inf和k>0。也许，更好的名称为k指数和尾部参数。在这里，alpha和U是众所周知的。 Y的平均 k * lower^k * (U^(1-k)-alpha^(1-k)) / ((1-k) * (1-(alpha/U)^k))。
值----------Value----------
An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm, and vgam.
类的一个对象"vglmff"（见vglmff-class）。该对象被用于建模功能，如vglm，vgam。
警告----------Warning ----------
The usual or unbounded Pareto distribution has two parameters (called alpha and k here) but the family function pareto1 estimates only k using iteratively reweighted least squares. The MLE of the alpha parameter lies on the boundary and is min(y) where y is the response. Consequently, using the default argument values, the standard errors are incorrect when one does a summary on the fitted object. If the user inputs a value for alpha then it is assumed known with this value and then summary on the fitted object should be correct. Numerical problems may occur for small k, e.g., k < 1.
通常的或无界的的帕累托分布有两个参数（称为alpha和k这里），但家庭的功能pareto1估计只有k使用迭代加权最小二乘法。 alpha参数的极大似然估计是在边界上，是min(y)y是响应。因此，使用默认参数值，标准差是不正确的，当一个人做了summary的合身的对象上。如果用户输入的值alpha然后假定与此值已知，，然后summary拟合对象上应该是正确的。小k，例如，k < 1数值可能会出现问题。
注意----------Note----------
Outside of economics, the Pareto distribution is known as the Bradford distribution.
以外的经济中，帕累托分布已知的布拉德福德分布。
For pareto1, if the estimate of k is less than or equal to unity then the fitted values will be NAs. Also, pareto1 fits the Pareto(I) distribution. See paretoIV for the more general Pareto(IV/III/II) distributions, but there is a slight change in notation: s = k and b = alpha.
对于pareto1，如果估计k是小于或等于1，那么对于拟合值将是NA的。另外，pareto1符合帕累托（I）的分布。见paretoIV对于更一般的帕累托分布（IV / III / II），但有一个微小的变化符号：s = k和b = alpha。
In some applications the Pareto law is truncated by a natural upper bound on the probability tail. The upper truncated Pareto distribution has three parameters (called alpha, U and k here) but the family function tpareto estimates only k. With known lower and upper limits, the ML estimator of k has the usual properties of MLEs. Aban (2006) discusses other inferential details.
在某些应用中，帕累托定律一个自然的上限的概率尾巴被截断。上截断Pareto分布有三个参数（称为alpha，U和k这里），但家庭功能tpareto估计只有k。与已知的上限和下限，最大似然估计的k具有通常的性能的最大似然估计。阿万（2006年）讨论了其他的推理细节。
（作者）----------Author(s)----------
T. W. Yee
参考文献----------References----------
Statistical Distributions, New York: Wiley-Interscience, Third edition.
Parameter estimation for the truncated Pareto distribution, Journal of the American Statistical Association, 101(473), 270–277.
参见----------See Also----------
Pareto, Tpareto, paretoIV, gpd.
Pareto，Tpareto，paretoIV，gpd。
实例----------Examples----------
alpha = 2; kay = exp(3)
pdat = data.frame(y = rpareto(n = 1000, location = alpha, shape = kay))
fit = vglm(y ~ 1, pareto1, pdat, trace = TRUE)
fit@extra # The estimate of alpha is here[估计这里的α]
head(fitted(fit))
with(pdat, mean(y))
coef(fit, matrix = TRUE)
summary(fit) # Standard errors are incorrect!![标准错误是不正确的！]
# Here, alpha is assumed known[在这里，α假定已知]
fit2 = vglm(y ~ 1, pareto1(location = alpha), pdat, trace = TRUE, crit = "coef")
fit2@extra # alpha stored here[阿尔法存储在这里]
head(fitted(fit2))
coef(fit2, matrix = TRUE)
summary(fit2) # Standard errors are okay[标准误差是可以的]
# Upper truncated Pareto distribution[上截断Pareto分布]
lower = 2; upper = 8; kay = exp(2)
pdat3 = data.frame(y = rtpareto(n = 100, lower = lower,
upper = upper, shape = kay))
fit3 = vglm(y ~ 1, tpareto1(lower, upper), pdat3, trace = TRUE, cri = "coef")
coef(fit3, matrix = TRUE)
c(fit3@misc$lower, fit3@misc$upper)
转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。
注：
注1：为了方便大家学习，本文档为生物统计家园网机器人LoveR翻译而成，仅供个人R语言学习参考使用，生物统计家园保留版权。
注2：由于是机器人自动翻译，难免有不准确之处，使用时仔细对照中、英文内容进行反复理解，可以帮助R语言的学习。
注3：如遇到不准确之处，请在本贴的后面进行回帖，我们会逐渐进行修订。
|
发表于 2012-10-1 15:46:34
